PI semigroup algebras of linear semigroups
- 1 January 1990
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 109 (1) , 39-46
- https://doi.org/10.1090/s0002-9939-1990-1013977-4
Abstract
It is well-known that if a semigroup algebra K [ S ] K[S] over a field K K satisfies a polynomial identity then the semigroup S S has the permutation property. The converse is not true in general even when S S is a group. In this paper we consider linear semigroups S ⊆ M n ( F ) S \subseteq {\mathcal {M}_n}(F) having the permutation property. We show then that K [ S ] K[S] has a polynomial identity of degree bounded by a fixed function of n n and the number of irreducible components of the Zariski closure of S S .Keywords
This publication has 16 references indexed in Scilit:
- Rewriting products of group elements—IIJournal of Algebra, 1988
- A Note on the PI-Property of Semigroup AlgebrasPublished by Springer Nature ,1988
- On cancellative semigroup ringsCommunications in Algebra, 1987
- On permutation properties in groups and semigroupsSemigroup Forum, 1986
- A permutational property of groupsArchiv der Mathematik, 1985
- On the burnside problem for semigroupsJournal of Algebra, 1984
- Semilocal semigroup ringsGlasgow Mathematical Journal, 1984
- Matrix SemigroupsProceedings of the American Mathematical Society, 1983
- Green's relations on a connected algebraic monoid†Linear and Multilinear Algebra, 1982
- Identities of semigroup algebras of 0-simple semigroupsSiberian Mathematical Journal, 1977